Identifying functions and using function notation

Lesson 4 and lab 1

• A relation is a pairing of input and output values

• The domain contains the input values.

• The range of a function or relation contains the output values.

• The input value, normally x, is the independent variable.

• The output, normally y, is called the dependent variable

Caution!!!!!

•In a function, the y values may repeat, the x values may not.

Function

• A function is a mapping between 2 sets that associates with each element of the first set, the domain, a unique (one and only one) element of the second set, the range.

Identifying functions

4-5

2

-1

6

3

Identifying functions, domain and range

4

33

2

-5

4

7

8

Vertical line test• When a relation is represented by a graph, the

vertical line test is used to determine if the relation is a function

Are these functions?

• It is sometimes necessary to work with more than one equation at a time.

• Function notation uses parentheses and letters to distinguish between equations

• The equation y= x + 2 can be written• f(x) = x+2• The equation y = x-5 can be written• g(x) = x-5• If I want to evaluate for x = 2, I would need to know

which equation I wanted to use. Functional notation tells me that.

• g(2) means I want to replace x with 2 in the g function, • So g(2) = 2-5 = -3 •

Using Function notation to evaluate functions• If h (x) = 4x-3 and p (x) = x2 -3x find p(-3)

• Use the "p" function

• p(-3) = (-3)2 -3(-3)

• = 9 +9

• = 18

Evaluate functions• If h (x) = -5x2 +2 and p (x) = x/2 -3x find h(-2)

Word problem• A company charges $.25 per minute for a cell phone

call. This can be expressed as the ordered pair (1, .25). Find the cost of a 2 minute call, 3-minute, and 4-minute call. Express the answers in set notation. Identify the domain and range. Determine if the set represents a function.

• 1 minute = (1, .25)• 2 minute = (2, .5)• 3 minute = (3, .75)• 4 minute = (4, 1)• Domain = 1,2,3,4, Range = .25, .5, .75, 1• Yes, function for every x value there is exactly one y

value

Problem• The company charges $.25 per minute for up to

3 minutes and then $.10 for every minute thereafter.

• Find the cost of a 2 minute, 3 minute and 4 minute call. Express the answers as ordered pairs.

• Find the domain and range.

• Is the set a function?

practice• 1. If a (x) = 9 + 6x and v (x) = 9x + 3x2, find v(2)

• 2. If you buy one ticket to a local baseball game, the cost is $25. This can be expressed as the ordered pair (1,25). There is a 1-day special if you buy ont ticket at regular price, each additional ticket is $20. Find the cost if you buy 2,3,and 4 tickets. Express the answers as ordered pairs in set notation. Identify the domain and range. Is the set a function?

practice• If you buy 1 t-shirt from your favorite store, the

cost is $15.50. This can be expressed as the ordered pair (1,15.50). The store is having a buy-one-get-one-free sale on t-shirts. For each shirt you buy you get the next one free. Find the total cost if you buy 2,3,4,5 and 6 t-shirts. Express the answers as ordered pairs in set notation.

• Identify the domain and range

• Is the set a function?

Lab 1-graphing a function and building a table• A graphing calculator can be used to analyze

functions.

• The calculator can be used to graph the function as well as build tables of data.

• Go to p. 19 Lab 1

• Follow the steps to graph and build a table.

• Do lab practice p. 20